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Properties

Label 96330cm
Number of curves $2$
Conductor $96330$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cm1")
 
E.isogeny_class()
 

Elliptic curves in class 96330cm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
96330.cr2 96330cm1 \([1, 1, 1, -13270, -2069293]\) \(-53540005609/350208000\) \(-1690387126272000\) \([2]\) \(645120\) \(1.6054\) \(\Gamma_0(N)\)-optimal
96330.cr1 96330cm2 \([1, 1, 1, -337750, -75531565]\) \(882774443450089/2166000000\) \(10454868294000000\) \([2]\) \(1290240\) \(1.9520\)  

Rank

sage: E.rank()
 

The elliptic curves in class 96330cm have rank \(1\).

Complex multiplication

The elliptic curves in class 96330cm do not have complex multiplication.

Modular form 96330.2.a.cm

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + 2 q^{7} + q^{8} + q^{9} + q^{10} - 4 q^{11} - q^{12} + 2 q^{14} - q^{15} + q^{16} + 4 q^{17} + q^{18} - q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.